Toric ideals of series and parallel connections of matroids
arXiv:1312.3428 · doi:10.1142/S0219498816501061
Abstract
In 1980, White conjectured that the toric ideal associated to a matroid is generated by binomials corresponding to a symmetric exchange. In this paper, we prove that classes of matroids for which the toric ideal is generated by quadrics and that has quadratic Gröbner bases, are closed under series and parallel extensions, series and parallel connections, and 2-sums.
10 pages